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<h1 id="_1">从代码注释生成</h1>


<div class="doc doc-object doc-module">


<a id="pyctrm.option.BS"></a>
  <div class="doc doc-contents first">

  

  <div class="doc doc-children">








<div class="doc doc-object doc-class">



<h2 id="pyctrm.option.BS.BS" class="doc doc-heading">
        <code>BS</code>


</h2>


  <div class="doc doc-contents ">

  
      <p>Black Scholes Model
Example:</p>
<p>K = 100;  r = 0.1 ;   T = 1 ;   sigma = 0.3 ;   S = np.arange(60,140,0.1)</p>

  <p><strong>Attributes:</strong></p>
  <table>
    <thead>
      <tr>
        <th>Name</th>
        <th>Type</th>
        <th>Description</th>
      </tr>
    </thead>
    <tbody>
        <tr>
          <td><code>S</code></td>
          <td>
          </td>
          <td><p>current asset price</p></td>
        </tr>
        <tr>
          <td><code>K</code></td>
          <td>
          </td>
          <td><p>strike price of the option</p></td>
        </tr>
        <tr>
          <td><code>r</code></td>
          <td>
          </td>
          <td><p>risk free rate</p></td>
        </tr>
        <tr>
          <td><code>T</code></td>
          <td>
          </td>
          <td><p>time until option expiration</p></td>
        </tr>
        <tr>
          <td><code>σ</code></td>
          <td>
          </td>
          <td><p>annualized volatility of the asset's returns</p></td>
        </tr>
        <tr>
          <td><code>q</code></td>
          <td>
          </td>
          <td><p>continuously compounded dividend ,0 to ignore dividend</p></td>
        </tr>
    </tbody>
  </table>

  <p><strong>Returns:</strong></p>
  <table>
    <thead>
      <tr>
<th>Name</th>        <th>Type</th>
        <th>Description</th>
      </tr>
    </thead>
    <tbody>
        <tr>
<td><code>Call</code></td>          <td>
          </td>
          <td><p>Call=S0<em>N(d1)</em>(e^-qT)-N(d2)K*(e^-rT)</p></td>
        </tr>
        <tr>
<td><code>Put</code></td>          <td>
          </td>
          <td><p>Put=N(-d2)<em>K</em>(e^-rT)-N(-d1)<em>S0</em>(e^-qT)</p></td>
        </tr>
        <tr>
<td><code>d1</code></td>          <td>
          </td>
          <td><p>d1=[ln(S/K)+(r-q+omega^2/2)<em>T]/[omega</em>(T^1/2)]</p></td>
        </tr>
        <tr>
<td><code>d2</code></td>          <td>
          </td>
          <td><p>d2=d1-omega*(T^1/2)</p></td>
        </tr>
    </tbody>
  </table>


        <details class="quote">
          <summary>Source code in <code>pyctrm\option\BS.py</code></summary>
          <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal"> 5</span>
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<span class="normal">69</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">class</span> <span class="nc">BS</span><span class="p">:</span>
    <span class="sd">&quot;&quot;&quot;Black Scholes Model</span>
<span class="sd">    Example:</span>

<span class="sd">    K = 100;  r = 0.1 ;   T = 1 ;   sigma = 0.3 ;   S = np.arange(60,140,0.1)</span>

<span class="sd">    Attributes:</span>
<span class="sd">        S : current asset price</span>
<span class="sd">        K: strike price of the option</span>
<span class="sd">        r: risk free rate</span>
<span class="sd">        T : time until option expiration</span>
<span class="sd">        σ: annualized volatility of the asset&#39;s returns</span>
<span class="sd">        q: continuously compounded dividend ,0 to ignore dividend</span>

<span class="sd">    Returns:</span>
<span class="sd">        Call: Call=S0*N(d1)*(e^-qT)-N(d2)K*(e^-rT)</span>
<span class="sd">        Put: Put=N(-d2)*K*(e^-rT)-N(-d1)*S0*(e^-qT)</span>
<span class="sd">        d1: d1=[ln(S/K)+(r-q+omega^2/2)*T]/[omega*(T^1/2)]</span>
<span class="sd">        d2: d2=d1-omega*(T^1/2)</span>

<span class="sd">    &quot;&quot;&quot;</span>

    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">S</span><span class="p">,</span> <span class="n">K</span><span class="p">,</span> <span class="n">T</span><span class="p">,</span> <span class="n">r</span><span class="p">,</span> <span class="n">sigma</span><span class="p">,</span> <span class="n">q</span><span class="o">=</span><span class="mi">0</span><span class="p">):</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">S</span> <span class="o">=</span> <span class="n">S</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">K</span> <span class="o">=</span> <span class="n">K</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">T</span> <span class="o">=</span> <span class="n">T</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">r</span> <span class="o">=</span> <span class="n">r</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">sigma</span> <span class="o">=</span> <span class="n">sigma</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">q</span> <span class="o">=</span> <span class="n">q</span>

    <span class="nd">@staticmethod</span>
    <span class="k">def</span> <span class="nf">N</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
        <span class="k">return</span> <span class="n">norm</span><span class="o">.</span><span class="n">cdf</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>

    <span class="nd">@property</span>
    <span class="k">def</span> <span class="nf">params</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
        <span class="k">return</span> <span class="p">{</span><span class="s1">&#39;S&#39;</span><span class="p">:</span> <span class="bp">self</span><span class="o">.</span><span class="n">S</span><span class="p">,</span>
                <span class="s1">&#39;K&#39;</span><span class="p">:</span> <span class="bp">self</span><span class="o">.</span><span class="n">K</span><span class="p">,</span>
                <span class="s1">&#39;T&#39;</span><span class="p">:</span> <span class="bp">self</span><span class="o">.</span><span class="n">T</span><span class="p">,</span>
                <span class="s1">&#39;r&#39;</span><span class="p">:</span> <span class="bp">self</span><span class="o">.</span><span class="n">r</span><span class="p">,</span>
                <span class="s1">&#39;q&#39;</span><span class="p">:</span> <span class="bp">self</span><span class="o">.</span><span class="n">q</span><span class="p">,</span>
                <span class="s1">&#39;sigma&#39;</span><span class="p">:</span> <span class="bp">self</span><span class="o">.</span><span class="n">sigma</span><span class="p">}</span>

    <span class="k">def</span> <span class="nf">d1</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
        <span class="k">return</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">S</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">K</span><span class="p">)</span> <span class="o">+</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">r</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">q</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">sigma</span> <span class="o">**</span> <span class="mi">2</span> <span class="o">/</span> <span class="mi">2</span><span class="p">)</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">T</span><span class="p">)</span> \
               <span class="o">/</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">sigma</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">T</span><span class="p">))</span>

    <span class="k">def</span> <span class="nf">d2</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">d1</span><span class="p">()</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">sigma</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">T</span><span class="p">)</span>

    <span class="k">def</span> <span class="nf">_call_value</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">S</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="bp">self</span><span class="o">.</span><span class="n">q</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">T</span><span class="p">)</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">N</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">d1</span><span class="p">())</span> <span class="o">-</span> \
               <span class="bp">self</span><span class="o">.</span><span class="n">K</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="bp">self</span><span class="o">.</span><span class="n">r</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">T</span><span class="p">)</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">N</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">d2</span><span class="p">())</span>

    <span class="k">def</span> <span class="nf">_put_value</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">K</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="bp">self</span><span class="o">.</span><span class="n">r</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">T</span><span class="p">)</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">N</span><span class="p">(</span><span class="o">-</span><span class="bp">self</span><span class="o">.</span><span class="n">d2</span><span class="p">())</span> <span class="o">-</span> \
               <span class="bp">self</span><span class="o">.</span><span class="n">S</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="bp">self</span><span class="o">.</span><span class="n">q</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">T</span><span class="p">)</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">N</span><span class="p">(</span><span class="o">-</span><span class="bp">self</span><span class="o">.</span><span class="n">d1</span><span class="p">())</span>

    <span class="k">def</span> <span class="nf">price</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">type_</span><span class="o">=</span><span class="s1">&#39;C&#39;</span><span class="p">):</span>
        <span class="k">if</span> <span class="n">type_</span> <span class="o">==</span> <span class="s1">&#39;C&#39;</span><span class="p">:</span>
            <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_call_value</span><span class="p">()</span>
        <span class="k">if</span> <span class="n">type_</span> <span class="o">==</span> <span class="s1">&#39;P&#39;</span><span class="p">:</span>
            <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_put_value</span><span class="p">()</span>
        <span class="k">else</span><span class="p">:</span>
            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s1">&#39;Unrecognized type&#39;</span><span class="p">)</span>
</code></pre></div></td></tr></table></div>
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